Flux quantization for a vortex in two-gap superconductor

Contrary to recent theoretical prediction, we show that the magnetic flux of a vortex in SU(2) model of two-gap superconductor is quantized in units of 2π/g, not 4π/g. For the U(1) version of this model, the flux is quantized in units of 2πα/g where 0 < α < 1. The parameter α depends on the masses and concentrations of the Cooper pairs in the two condensates. PACS number(s): 74.20.De, 74.25.Qt, 74.25.Sv, 74.90.+n Ginzburg-Landau models with two flavors of Cooper pairs have attracted increased attention in recent years [1-3]. The discovery [4] of the two-band superconductor MgB2 with surprisingly high transition temperature has sparked renewed interest in these models. Starting from a Lagrangian for a charged doublet order parameter exhibiting SU(2) symmetry, Cho [2] studied the flux quantization for a magnetic vortex. In his approach , the magnetic flux is related to the boundary values of the gauge field at r = 0 and r = ∞ where r is the distance from the vortex center. The r = 0 value is determined by examining the equation of motion for the magnitude of the order parameter. Smothness of the order parameter at r = 0 requires that this boundary value is nonzero. Consequently, the flux is predicted in Ref. [2] to be quantized in the unit 4π/g which is double of the flux carried by the well known Abrikosov vortex in one-gap superconductor [5]. In the present paper, we consider the same SU(2) model of two-gap superconductor and calculate the magnetic flux for the vortex in terms of the Berry connection that is due to the texture induced by the vortex in the charge space [2, 3]. In this way, we find that the vortex has a total flux quantized in the same unit as the Abelian vortex in one-gap superconductor. Moreover, the present method allows us to consider the flux quantization in a more realistic U(1) model of the two-gap superconductor. In this model the flux appears to be quantized in the unit of 2π/g times a parameter that can take any value in Electronic address: [email protected]